Update from my post #49. The diagnostic is that the new injector #2 is bad. I told the SA that there is a possibility of carbon built-up and it is unlikely the problem is the new injector. He agree but cannot check for it. They have to follow the BMW NA protocol and diagnostic, they are replacing injector #2 for a second time. With my permission, they are keeping and driving the car for 2 more days to make sure the fault is cleared this time. In the mean time I got a 2013 X5.

Yes, unfortunately that is their protocol. First all has to be well (injectors, fuel system, etc.), then you have to get code(s) for "insufficient flow", "smooth running controller" in cyl X. THEN they will start checking for carbon. Time consuming and frustrating process, but that is BMW's diagnostic methods.